After a long time in sleep mode when I have used the power button to put it to sleep, my iMac suddenly turns on when I am no where near my computer. It shows the crash message screen and then reboots.
This has happened at least three times and I am beginning to get concerned. Might be the same issue as intentionally resuming from sleep but what is weird is that it happens randomly and unattended.
I have the same issue with my iMac. I am using 10.8.2 and it all started when I bought a D-link switch and plug the network cable directly to the switch. I was using WIFI connection before and did not have any problems. The symptom is it will work normally when the computer is running, but when it sleeps for awhile it will crash and I will see a login screen similar to the first bootup screen. The crash report (Kernel Panic) will show up indicating that I did not do a shutdown properly.
I tried to remove the network cable and tested for another day without any problem. I realized it might be the new switch causing problems during sleep mode and I am trying to connect it directly to Airport Extreme 5th edition. So far after a day's usage and no problem so far.
You can try to see if using WIFI will work and then troubleshoot the router / switch that you are connecting directly to it. Sometimes, the MAC may be picky on the type of hardware it is connecting to.